{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cdf6664d-8193-4491-98a4-8a6de371fe0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Exam1</th>\n",
       "      <th>Exam2</th>\n",
       "      <th>Pass</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>34.623660</td>\n",
       "      <td>78.024693</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>30.286711</td>\n",
       "      <td>43.894998</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>35.847409</td>\n",
       "      <td>72.902198</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>60.182599</td>\n",
       "      <td>86.308552</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>79.032736</td>\n",
       "      <td>75.344376</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Exam1      Exam2  Pass\n",
       "0  34.623660  78.024693     0\n",
       "1  30.286711  43.894998     0\n",
       "2  35.847409  72.902198     0\n",
       "3  60.182599  86.308552     1\n",
       "4  79.032736  75.344376     1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# 读取数据\n",
    "data = pd.read_csv('examdata.csv')\n",
    "data.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c1a98ba7-33fb-49f1-a284-6125111efd82",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 可视化数据\n",
    "# 启用嵌入显示功能\n",
    "\n",
    "%matplotlib inline \n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "fig1 = plt.figure()\n",
    "e1 = data.loc[:,'Exam1']\n",
    "e2 = data.loc[:,'Exam2']\n",
    "\n",
    "plt.scatter(e1, e2, c = 'hotpink')\n",
    "plt.title('Exam1 - Exam2')\n",
    "plt.xlabel('Exam1')\n",
    "plt.ylabel('Exam2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ce5d8a66-3f05-43fa-ab2b-7d969a23c725",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0     False\n",
      "1     False\n",
      "2     False\n",
      "3      True\n",
      "4      True\n",
      "      ...  \n",
      "95     True\n",
      "96     True\n",
      "97     True\n",
      "98     True\n",
      "99     True\n",
      "Name: Pass, Length: 100, dtype: bool\n"
     ]
    }
   ],
   "source": [
    "# add lable mask\n",
    "mask = data.loc[:,'Pass'] == 1\n",
    "print(mask)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "d72f6205-12fb-4b32-88b5-44370d4c786f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig2 = plt.figure(facecolor='w')\n",
    "\n",
    "plt.gca().set_facecolor('black') \n",
    "# 根据上面的标签mask来区分不同的点，如果不给出颜色，也是自动换成连个颜色的\n",
    "passed = plt.scatter(data.loc[:,'Exam1'][mask], data.loc[:,'Exam2'][mask], c = 'green')\n",
    "failed = plt.scatter(data.loc[:,'Exam1'][~mask], data.loc[:,'Exam2'][~mask], c = 'pink')\n",
    "plt.legend((passed,failed),('passed','failed'))\n",
    "\n",
    "plt.title('Exam1(X-Label) - Exam2(Y-Label)')\n",
    "plt.xlabel('Exam1')\n",
    "plt.ylabel('Exam2')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "01000053-f27c-4c08-9274-df1dc2fcc3e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 定义数据，用于训练\n",
    "\n",
    "X = data.drop(['Pass'],axis = 1) # 从data中剥离结果\n",
    "y = data.loc[:,'Pass']\n",
    "\n",
    "X1 = data.loc[:,'Exam1']\n",
    "X2 = data.loc[:,'Exam2']\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "bb8c71c0-87f8-4824-b9ac-82f0fad304ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 2) (100,)\n"
     ]
    }
   ],
   "source": [
    "print(X.shape, y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "5ae71140-c32e-4ee0-802e-d0b592ca0375",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: #000;\n",
       "  --sklearn-color-text-muted: #666;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: flex;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "  align-items: start;\n",
       "  justify-content: space-between;\n",
       "  gap: 0.5em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label .caption {\n",
       "  font-size: 0.6rem;\n",
       "  font-weight: lighter;\n",
       "  color: var(--sklearn-color-text-muted);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 0.5em;\n",
       "  text-align: center;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>LogisticRegression</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.linear_model.LogisticRegression.html\">?<span>Documentation for LogisticRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\"><pre>LogisticRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# establish the model and train it\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "LR = LogisticRegression()\n",
    "print(X.shape)\n",
    "LR.fit(X,y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "bf3d2d0b-813a-452c-b41b-7d1470271fb9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1\n",
      " 1 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1\n",
      " 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1]\n"
     ]
    }
   ],
   "source": [
    "#show predicted result and its accuracy\n",
    "y_predict = LR.predict(X)\n",
    "print(y_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "14a8fba5-6a6d-474a-ab62-0761725c5ae7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.89\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "accuracy = accuracy_score(y, y_predict)\n",
    "print(accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "50912564-36a8-475e-9162-1f22d8386f98",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 2)\n",
      "passed\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/cc/miniconda3/envs/TF_GPU/lib/python3.10/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "# Exam1 70, Exam2 65\n",
    "x_test = np.array([70,65]).reshape(1,-1)\n",
    "\n",
    "print(x_test.shape)\n",
    "\n",
    "y_test = LR.predict(x_test)\n",
    "print('passed' if y_test == 1 else 'failed')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "f2b7f196-bd7a-43cb-af58-f42e1a7d99dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.20535491, 0.2005838 ]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LR.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "67dcb925-5e8b-45bf-bca4-05c78940b49f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-25.05219314])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LR.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "3254f1b8-dbc0-4387-afdd-f7c992c7e3bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-25.05219314] 0.20535491217790375 0.2005838039546904\n"
     ]
    }
   ],
   "source": [
    "theta0 = LR.intercept_\n",
    "theta1 = LR.coef_[0][0]\n",
    "theta2 = LR.coef_[0][1]\n",
    "\n",
    "print(theta0, theta1, theta2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "e8eeed39-86c0-4dbe-8dcb-187b7e86bcba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0     89.449169\n",
      "1     93.889277\n",
      "2     88.196312\n",
      "3     63.282281\n",
      "4     43.983773\n",
      "        ...    \n",
      "95    39.421346\n",
      "96    81.629448\n",
      "97    23.219064\n",
      "98    68.240049\n",
      "99    48.341870\n",
      "Name: Exam1, Length: 100, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "X2_NEW = (-theta0 - theta1 * X1)/theta2\n",
    "print(X2_NEW)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "937682a1-ae27-4fa6-9f67-ef52dbb7a42e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig3 = plt.figure()\n",
    "plt.plot(X1, X2_NEW)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "bd7fb184-1538-487b-b3b9-2b79d3dd68b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta0 = LR.intercept_\n",
    "theta1 = LR.coef_[0][0]\n",
    "theta2 = LR.coef_[0][1]\n",
    "X1_NEW = (-theta0 - theta2 * X2)/theta1\n",
    "\n",
    "fig4 = plt.figure()\n",
    "plt.plot(X1_NEW, X2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c57ec86b-2e4d-4bb1-809b-7976d94ba011",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "3f3d00cb-127b-41f4-aef4-19bb6edffa8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig5 = plt.figure()\n",
    "plt.plot(X1, X2_NEW)\n",
    "\n",
    "passed = plt.scatter(data.loc[:,'Exam1'][mask], data.loc[:,'Exam2'][mask])\n",
    "failed = plt.scatter(data.loc[:,'Exam1'][~mask], data.loc[:,'Exam2'][~mask])\n",
    "plt.title('Exam1 - Exam2')\n",
    "plt.xlabel('Exam1')\n",
    "plt.ylabel('Exam2')\n",
    "plt.legend((passed,failed),('passed','failed'))\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2ed70fc3-dfd7-4132-abfc-0b8790e00a85",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "251610aa-37eb-436d-8627-a0266355da73",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "91ffc24a-88a0-417f-8bff-cfdb30aa9a94",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           X1         X2         X1_2         X2_2        X1_X2\n",
      "0   34.623660  78.024693  1198.797805  6087.852690  2701.500406\n",
      "1   30.286711  43.894998   917.284849  1926.770807  1329.435094\n",
      "2   35.847409  72.902198  1285.036716  5314.730478  2613.354893\n",
      "3   60.182599  86.308552  3621.945269  7449.166166  5194.273015\n",
      "4   79.032736  75.344376  6246.173368  5676.775061  5954.672216\n",
      "..        ...        ...          ...          ...          ...\n",
      "95  83.489163  48.380286  6970.440295  2340.652054  4039.229555\n",
      "96  42.261701  87.103851  1786.051355  7587.080849  3681.156888\n",
      "97  99.315009  68.775409  9863.470975  4730.056948  6830.430397\n",
      "98  55.340018  64.931938  3062.517544  4216.156574  3593.334590\n",
      "99  74.775893  89.529813  5591.434174  8015.587398  6694.671710\n",
      "\n",
      "[100 rows x 5 columns]\n"
     ]
    }
   ],
   "source": [
    "# 二级边界函数\n",
    "# 创建新的数据\n",
    "\n",
    "X1_2 = X1 * X1\n",
    "X2_2 = X2 * X2\n",
    "X1_X2 = X1 * X2\n",
    "X_new = {'X1':X1,'X2':X2,'X1_2':X1_2,'X2_2':X2_2,'X1_X2':X1_X2}\n",
    "X_new = pd.DataFrame(X_new)\n",
    "print(X_new)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "6e52ebc2-449e-4fe3-8c89-803dac19c649",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/cc/miniconda3/envs/TF_GPU/lib/python3.10/site-packages/sklearn/linear_model/_logistic.py:465: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
      "STOP: TOTAL NO. OF ITERATIONS REACHED LIMIT.\n",
      "\n",
      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
      "Please also refer to the documentation for alternative solver options:\n",
      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
      "  n_iter_i = _check_optimize_result(\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-5 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: #000;\n",
       "  --sklearn-color-text-muted: #666;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-5 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-5 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-5 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: flex;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "  align-items: start;\n",
       "  justify-content: space-between;\n",
       "  gap: 0.5em;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 label.sk-toggleable__label .caption {\n",
       "  font-size: 0.6rem;\n",
       "  font-weight: lighter;\n",
       "  color: var(--sklearn-color-text-muted);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-5 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-5 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-5 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-5 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-5 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-5 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-5 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-5 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 0.5em;\n",
       "  text-align: center;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-5 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-5 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-5\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" checked><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>LogisticRegression</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.linear_model.LogisticRegression.html\">?<span>Documentation for LogisticRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\"><pre>LogisticRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#创建新的模型\n",
    "LR2 = LogisticRegression()\n",
    "LR2.fit(X_new, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "0f826b79-0058-4bf5-b611-928c921852ef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0\n",
      " 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1\n",
      " 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1]\n",
      "1.0\n"
     ]
    }
   ],
   "source": [
    "y2_predict = LR2.predict(X_new)\n",
    "print(y2_predict)\n",
    "\n",
    "from sklearn.metrics import accuracy_score\n",
    "accuracy2 = accuracy_score(y, y2_predict)\n",
    "print(accuracy2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "f158ca12-6da3-4ffa-9084-e63b83ce4aa8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.73561533, -1.38527195, -0.00156763,  0.00351538,  0.03962666]])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 可视化\n",
    "LR2.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "1d6a6ac7-d946-4ae3-b430-7348386d0bf5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-15.55898715] -0.7356153255119906 -1.3852719457375315 -0.001567631808426605 0.0035153820988638555 0.039626663391560596\n"
     ]
    }
   ],
   "source": [
    "theta0 = LR2.intercept_\n",
    "theta1 = LR2.coef_[0][0]\n",
    "theta2 = LR2.coef_[0][1]\n",
    "theta3 = LR2.coef_[0][2]\n",
    "theta4 = LR2.coef_[0][3]\n",
    "theta5 = LR2.coef_[0][4]\n",
    "print(theta0,theta1,theta2,theta3,theta4,theta5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "e002d29e-cae6-4682-b738-5816f0eaaf0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X2_sort = X2.sort_values()\n",
    "a = theta3\n",
    "b = theta1+theta5*X2_sort\n",
    "c = theta0+theta2*X2_sort+theta4*X2_sort*X2_sort \n",
    "x1_new_boundary = (-b+np.sqrt(b*b-4*a*c))/(2*a)\n",
    "x1_new_boundary.head()\n",
    "fig6 = plt.figure()\n",
    "plt.plot(x1_new_boundary,X2_sort)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "a85802da-8602-4827-9943-25aa8e879e40",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0     34.623660\n",
      "1     30.286711\n",
      "2     35.847409\n",
      "3     60.182599\n",
      "4     79.032736\n",
      "        ...    \n",
      "95    83.489163\n",
      "96    42.261701\n",
      "97    99.315009\n",
      "98    55.340018\n",
      "99    74.775893\n",
      "Name: Exam1, Length: 100, dtype: float64 63    30.058822\n",
      "1     30.286711\n",
      "57    32.577200\n",
      "70    32.722833\n",
      "36    33.915500\n",
      "        ...    \n",
      "56    97.645634\n",
      "47    97.771599\n",
      "51    99.272527\n",
      "97    99.315009\n",
      "75    99.827858\n",
      "Name: Exam1, Length: 100, dtype: float64\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAigAAAGdCAYAAAA44ojeAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjAsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvlHJYcgAAAAlwSFlzAAAPYQAAD2EBqD+naQAAP6tJREFUeJzt3Xl8VNX9//H3TJbJPtknmZBA2EQIO4IgCiriAq51A7Wg1mq1auqGaFu1tVD1W5cWl2oXFKvYVvGnuLCpICIIYd9BQggkISzZl8ky9/dHYGrYJDDJncy8no/HfYTce2fyOdfAvD33nHMthmEYAgAA8CFWswsAAAA4EgEFAAD4HAIKAADwOQQUAADgcwgoAADA5xBQAACAzyGgAAAAn0NAAQAAPifY7AJOhdvtVkFBgaKjo2WxWMwuBwAAnATDMFRRUSGn0ymr9cR9JO0yoBQUFCg9Pd3sMgAAwCnIz89Xhw4dTnhOiwPKokWL9NxzzyknJ0eFhYWaNWuWrrrqqmOee+edd+r111/XCy+8oOzsbM9+l8ulhx56SO+++65qamp04YUX6pVXXvnRYg+Ljo6W1NTAmJiYljYBAACYoLy8XOnp6Z7P8RNpcUCpqqpS3759deutt+onP/nJcc/78MMPtWzZMjmdzqOOZWdn6+OPP9bMmTOVkJCgBx98UGPHjlVOTo6CgoJ+tIbDt3ViYmIIKAAAtDMnMzyjxQHl0ksv1aWXXnrCc/bs2aNf/vKXmjNnjsaMGdPsWFlZmf7+979rxowZGjVqlCTp7bffVnp6uubPn6+LL764pSUBAAA/4/VZPG63W7fccosefvhh9erV66jjOTk5qq+v1+jRoz37nE6nsrKytGTJkmO+p8vlUnl5ebMNAAD4L68HlGeeeUbBwcG67777jnm8qKhIoaGhiouLa7bf4XCoqKjomK+ZOnWq7Ha7Z2OALAAA/s2rASUnJ0cvvfSSpk+f3uLpv4ZhHPc1kydPVllZmWfLz8/3RrkAAMBHeTWgfP311youLlZGRoaCg4MVHBysvLw8Pfjgg+rUqZMkKSUlRXV1dSopKWn22uLiYjkcjmO+r81m8wyIZWAsAAD+z6sB5ZZbbtHatWu1evVqz+Z0OvXwww9rzpw5kqSBAwcqJCRE8+bN87yusLBQ69ev17Bhw7xZDgAAaKdaPIunsrJS27dv93yfm5ur1atXKz4+XhkZGUpISGh2fkhIiFJSUnTGGWdIkux2u26//XY9+OCDSkhIUHx8vB566CH17t3bM6sHAAAEthYHlBUrVuj888/3fP/AAw9IkiZMmKDp06ef1Hu88MILCg4O1vXXX+9ZqG369OkntQYKAADwfxbDMAyzi2ip8vJy2e12lZWVMR4FAIB2oiWf3zzNGAAA+BwCCgAA8DkEFAAA4HNaPEjWnxWV1eq95fmqqW/Uo5f2MLscAAACFj0oP7C/0qUX5m/Vm0t2qra+0exyAAAIWASUH+jljFFabLhq6hu1aOs+s8sBACBgEVB+wGKxaHSvpuX252zYa3I1AAAELgLKES7ulSJJWrB5rxoa3SZXAwBAYCKgHOGsTvGKjwxVaXW9luUeNLscAAACEgHlCEFWiy46s+k2z6frCk2uBgCAwERAOYYxfVIlSZ+vL+I2DwAAJiCgHMOwLgmKiwjRgao6Ld3BbR4AANoaAeUYgoOsuiSrqRdl9toCk6sBACDwEFCO4/LDt3k2FKme2zwAALQpAspxDM6MV2JU02yeb7bvN7scAAACCgHlOIKDrLr00G2eT9YymwcAgLZEQDmBw7N55mwoUl0Dt3kAAGgrBJQTOKtTvJKjbSqvbdDi7TybBwCAtkJAOYEgq0WX9T40m2cNt3kAAGgrBJQfMfbQbZ55G/eqtr7R5GoAAAgMBJQfMSAjTikxYapwNWjRVm7zAADQFggoP8JqtXgGy37Cs3kAAGgTBJSTcDigzOc2DwAAbYKAchL6p8cqLTZcVXWN+mpLsdnlAADg9wgoJ8Fi+d9tno9ZtA0AgFZHQDlJh2fzfLGpWNV1DSZXAwCAfyOgnKTeaXZlxEeopr5RX2zmNg8AAK2JgHKSfnibh2fzAADQuggoLTDm0KqyX2wuVqWL2zwAALQWAkoL9HLGKDMxUq4GtxZs2mt2OQAA+C0CSgtYLBZPL8psbvMAANBqCCgtNLZvU0BZuGWfymvrTa4GAAD/REBpoTMc0eqSFKm6Rrfmb+Q2DwAArYGA0kIWi0Vj+zglcZsHAIDWQkA5BYcXbft62z6VVXObBwAAbyOgnIJujmid4YhWfaOhORuLzC4HAAC/Q0A5RSzaBgBA6yGgnKLDAeWb7ftVUlVncjUAAPgXAsop6pIUpTNTY9TgNjRnA7d5AADwJgLKaTg8WJbZPAAAeBcB5TQcDihLvt+vA5Uuk6sBAMB/EFBOQ8eESPVOs8ttSJ+t5zYPAADeQkA5TczmAQDA+wgop+nwwwOX5R5QcUWtydUAAOAfCCinKT0+Qn3TY+U2pM+5zQMAgFcQULzg8sOzedZwmwcAAG8goHjBZYdu8yzPO6iiMm7zAABwuggoXuCMDdfAjnEyDOnTdfSiAABwuggoXnJ4sOwnBBQAAE4bAcVLLuudKotFyskrUUFpjdnlAADQrhFQvCTFHqazOsZL4jYPAACni4DiRWP7Nt3m+ZhF2wAAOC0EFC+6JCtFVou0Jr9U+QerzS4HAIB2i4DiRcnRYRraJUGS9P9W7zG5GgAA2i8Cipdd1S9NkvTBqj0yDMPkagAAaJ8IKF52ae9UhYVYtWNfldbsLjO7HAAA2iUCipdF2YJ1Sa8USdL7ObtNrgYAgPaJgNIKrh2YLkn6aE2BausbTa4GAID2p8UBZdGiRbr88svldDplsVj04Ycfeo7V19dr0qRJ6t27tyIjI+V0OvXTn/5UBQUFzd7D5XLp3nvvVWJioiIjI3XFFVdo927/6W0Y2iVBTnuYymrqtWBTsdnlAADQ7rQ4oFRVValv376aNm3aUceqq6u1cuVK/eY3v9HKlSv1wQcfaOvWrbriiiuanZedna1Zs2Zp5syZWrx4sSorKzV27Fg1NvpHb0OQ1aJrBnSQJP03J9/kagAAaH8sxmlMNbFYLJo1a5auuuqq456zfPlyDR48WHl5ecrIyFBZWZmSkpI0Y8YM3XDDDZKkgoICpaen69NPP9XFF1981Hu4XC65XC7P9+Xl5UpPT1dZWZliYmJOtfxWlbu/Suf/31eyWqSlky9UckyY2SUBAGCq8vJy2e32k/r8bvUxKGVlZbJYLIqNjZUk5eTkqL6+XqNHj/ac43Q6lZWVpSVLlhzzPaZOnSq73e7Z0tPTW7vs05aZGKlBHePkNqRZq1gTBQCAlmjVgFJbW6tHH31U48eP9ySloqIihYaGKi4urtm5DodDRUVFx3yfyZMnq6yszLPl57eP2ybXDmy6zfOfnN2siQIAQAu0WkCpr6/XjTfeKLfbrVdeeeVHzzcMQxaL5ZjHbDabYmJimm3twWV9mtZE2V5cyZooAAC0QKsElPr6el1//fXKzc3VvHnzmgWKlJQU1dXVqaSkpNlriouL5XA4WqMc08SEhXjWRGGwLAAAJ8/rAeVwONm2bZvmz5+vhISEZscHDhyokJAQzZs3z7OvsLBQ69ev17Bhw7xdjuk8a6KsZk0UAABOVnBLX1BZWant27d7vs/NzdXq1asVHx8vp9Opa6+9VitXrtTs2bPV2NjoGVcSHx+v0NBQ2e123X777XrwwQeVkJCg+Ph4PfTQQ+rdu7dGjRrlvZb5iMNrohSU1Wr+pr0a28dpdkkAAPi8FvegrFixQv3791f//v0lSQ888ID69++v3/72t9q9e7c++ugj7d69W/369VNqaqpn++EMnRdeeEFXXXWVrr/+ep1zzjmKiIjQxx9/rKCgIO+1zEc0XxPFfxajAwCgNZ3WOihmack8al/wwzVRvp18oRysiQIACEA+tQ4KWBMFAICWIqC0kcNrovyXNVEAAPhRBJQ2MoY1UQAAOGkElDYSHRaiS7NSJbEmCgAAP4aA0oYO3+ZhTRQAAE6MgNKGhnZuWhOlvLZB8zftNbscAAB8FgGlDVmtFv3k8AMEV7AmCgAAx0NAaWM/ObRo26Jt+1RQWmNyNQAA+CYCShvrlBipszvHyzDoRQEA4HgIKCYYNzhDkvTvFflqdLMmCgAARyKgmODiXimyh4doT2mNFm/fb3Y5AAD4HAKKCcJCgnR1/zRJ0rvLdplcDQAAvoeAYpIbB6dLkuZv2qviilqTqwEAwLcQUEzSIyVGAzJi1eA29N8cBssCAPBDBBQTHR4sO/O7fLkZLAsAgAcBxURj+zgVHRasXQer9c33DJYFAOAwAoqJwkODdM2hwbLvMFgWAAAPAorJxg1pus0zbyODZQEAOIyAYrIfDpZ977t8s8sBAMAnEFB8wM1nd5QkvfvdLjU0uk2uBgAA8xFQfMBlvVMVFxGigrJafbG52OxyAAAwHQHFB4SFBOn6s5oWbpuxNM/kagAAMB8BxUfcNLijLBbp6237tXN/ldnlAABgKgKKj8hIiNDI7kmSpH8toxcFABDYCCg+5JahTYNl/71it2rrG02uBgAA8xBQfMiI7snqEBeuspp6fbymwOxyAAAwDQHFhwRZLbppSFMvytsMlgUABDACio+5flAHhQZZtWZ3mdbkl5pdDgAApiCg+JiEKJvG9EmVxJRjAEDgIqD4oMMry360pkAHKl0mVwMAQNsjoPigARmx6tPBrroGt2Yu5/k8AIDAQ0DxQRaLRROHdZIkzfg2T/U8nwcAEGAIKD5qTJ9UJUbZVFReq8/XF5ldDgAAbYqA4qNswUG6aUiGJGn6kp3mFgMAQBsjoPiwm4ZkKCTIopy8Eq3dXWp2OQAAtBkCig9LjgnTmN5NU47pRQEABBICio+beE6mJGn2mkLtq2DKMQAgMBBQfFy/9Fj1S49VXaNb05fkml0OAABtgoDSDtw1oosk6a0leSqrqTe5GgAAWh8BpR0Y3dOh7o4oVbgaNOPbnWaXAwBAqyOgtANWq0V3j+wqSfr74lxV1zWYXBEAAK2LgNJOjO2Tqoz4CJVU1+udZbvMLgcAgFZFQGkngoOs+sXIprEob3y9Q66GRpMrAgCg9RBQ2pFrBqQpJSZMe8td+m/ObrPLAQCg1RBQ2hFbcJB+fl5nSdJrC79XAw8RBAD4KQJKOzNucIYSIkOVf7BGH60pMLscAABaBQGlnQkPDdJtw5tWl33lq+/ldhsmVwQAgPcRUNqhW4Z2VHRYsLYXV2rOhiKzywEAwOsIKO1QTFiIJg7rJEma9uV2GQa9KAAA/0JAaaduPSdT4SFB2lBQrq+27jO7HAAAvIqA0k7FR4bqpiEZkqSXv6AXBQDgXwgo7dgd53VWaJBVK/JKtCz3oNnlAADgNQSUdswRE6brBnWQJL385XaTqwEAwHsIKO3cXSO6KMhq0dfb9mtNfqnZ5QAA4BUElHYuPT5CV/ZzSqIXBQDgPwgofuDukV1ksUhzN+7VlqIKs8sBAOC0EVD8QNfkaF3SK0WS9MpX9KIAANq/FgeURYsW6fLLL5fT6ZTFYtGHH37Y7LhhGHryySfldDoVHh6ukSNHasOGDc3Ocblcuvfee5WYmKjIyEhdccUV2r2bp/OejnvO7ypJ+nhNgXburzK5GgAATk+LA0pVVZX69u2radOmHfP4s88+q+eff17Tpk3T8uXLlZKSoosuukgVFf+79ZCdna1Zs2Zp5syZWrx4sSorKzV27Fg1NjaeeksCXFaaXSPPSJLbaHrSMQAA7ZnFOI0VviwWi2bNmqWrrrpKUlPvidPpVHZ2tiZNmiSpqbfE4XDomWee0Z133qmysjIlJSVpxowZuuGGGyRJBQUFSk9P16effqqLL774R39ueXm57Ha7ysrKFBMTc6rl+50VOw/q2te+VUiQRQsfPl/O2HCzSwIAwKMln99eHYOSm5uroqIijR492rPPZrNpxIgRWrJkiSQpJydH9fX1zc5xOp3KysrynHMkl8ul8vLyZhuONqhTvIZkxqu+0dDri3aYXQ4AAKfMqwGlqKjpyboOh6PZfofD4TlWVFSk0NBQxcXFHfecI02dOlV2u92zpaene7Nsv/LLC5rGosxcvkv7K10mVwMAwKlplVk8Foul2feGYRy170gnOmfy5MkqKyvzbPn5+V6r1d8M75qovh3sqq136++Lc80uBwCAU+LVgJKS0jTV9ciekOLiYk+vSkpKiurq6lRSUnLcc45ks9kUExPTbMOxWSwWz4yeGd/mqay63uSKAABoOa8GlMzMTKWkpGjevHmefXV1dVq4cKGGDRsmSRo4cKBCQkKanVNYWKj169d7zsHpGXWmQ2c4olXpatCb3+40uxwAAFqsxQGlsrJSq1ev1urVqyU1DYxdvXq1du3aJYvFouzsbE2ZMkWzZs3S+vXrNXHiREVERGj8+PGSJLvdrttvv10PPvigFixYoFWrVunmm29W7969NWrUKK82LlBZrRbdfX4XSdI/vslVlavB5IoAAGiZ4Ja+YMWKFTr//PM93z/wwAOSpAkTJmj69Ol65JFHVFNTo7vvvlslJSUaMmSI5s6dq+joaM9rXnjhBQUHB+v6669XTU2NLrzwQk2fPl1BQUFeaBIkaWwfp16Yt1U7D1TrnWW7dMd5nc0uCQCAk3Za66CYhXVQTs57y3dp0vvrlBRt09ePnK+wEAIgAMA8pq2DAt9ydf8OctrDtK/Cpf/k8CgBAED7QUDxY6HBVv380K2d1776XvWNbpMrAgDg5BBQ/NyNgzOUGBWqPaU1+n+rC8wuBwCAk0JA8XNhIUG6fXhTL8orX21Xo7vdDTkCAAQgAkoAuPnsDMWEBWvHvip9vv7YjxMAAMCXEFACQHRYiCaekylJmvbldrXDiVsAgABDQAkQtw7rpIjQIG0qLNeXW4rNLgcAgBMioASIuMhQ3Xx2R0nStC/oRQEA+DYCSgD52fBMhQZbtXJXqb7ZfsDscgAAOC4CSgBJjgnT+MEZkqRnPt8sNzN6AAA+ioASYH55QVdF2YK1bk+ZZq8rNLscAACOiYASYBKjbLrz0Oqyz83ZLFdDo8kVAQBwNAJKALr93EwlR9uUf7BG/1q6y+xyAAA4CgElAEWEBit7VHdJ0l++2Kby2nqTKwIAoDkCSoC6flAHdUmKVEl1vf668HuzywEAoBkCSoAKDrLqkUt6SJL+vjhXRWW1JlcEAMD/EFAC2OieDg3sGKfaerdenL/V7HIAAPAgoAQwi8Wixy5r6kX594p8bSmqMLkiAACaEFAC3MCO8bqkV4rchvT0JxtZAh8A4BMIKNDky3ooNMiqr7ft1xebeZAgAMB8BBSoY0Kkbh3eSZL0h082qa7BbW5BAICAR0CBJOmX53dVYlSoduyv0oyleWaXAwAIcAQUSJKiw0L00OgzJEkvzd+qg1V1JlcEAAhkBBR4XDcoXWemxqi8tkEvzGPaMQDAPAQUeARZLfrN2DMlSf9alse0YwCAaQgoaGZYl0Rd3MshtyH9fjbTjgEA5iCg4CiPXXamQoOtWrx9v+ZsKDK7HABAACKg4CgdEyL183M7S5J+P3uTauoaTa4IABBoCCg4prvP7yKnPUx7Smv05y+2mV0OACDAEFBwTBGhwXrqyixJ0huLdmhzUbnJFQEAAgkBBcd1UU+HLu7lUIPb0OQP1sntZsAsAKBtEFBwQk9dkaUoW7BW7SrVv77bZXY5AIAAQUDBCaXYw/TQ6O6SpGc/26y95bUmVwQACAQEFPyoW4Z2Ut8OdlW4GvS7jzeaXQ4AIAAQUPCjgqwWTbmmt4KsFn2yrlBfbN5rdkkAAD9HQMFJ6eW06/bhmZKk33y4QdV1DSZXBADwZwQUnLTsUd2UFhuuPaU1PEwQANCqCCg4aRGhwXr6qqa1Uf7xzU6t31NmckUAAH9FQEGLnN8jWWP6pKrRbeixWevUyNooAIBWQEBBiz0xtqeiw4K1dneZZny70+xyAAB+iICCFkuOCdOkS3pIkp6bs0WFZTUmVwQA8DcEFJyS8YMzNCAjVlV1jXri/20wuxwAgJ8hoOCUWA+tjRJstWjuxr2as6HI7JIAAH6EgIJT1iMlRnec11mS9ORHG1TpYm0UAIB3EFBwWu67oJsy4iNUWFarZz/fbHY5AAA/QUDBaQkPDdIfrm5aG+Wtb/O0dMcBkysCAPgDAgpO27ndkjRucLok6cF/r1FZTb3JFQEA2jsCCrziscvOVEZ8hPaU1uixD9bJMFjADQBw6ggo8IrosBD9eVx/BR964vF7y/PNLgkA0I4RUOA1/dJj9dDFZ0iSnvx4g7btrTC5IgBAe0VAgVf9/NzOOrdbomrr3br33VWqrW80uyQAQDtEQIFXWa0W/en6vkqMCtXmogpN+XST2SUBANohAgq8Ljk6TH+6vp+kpqnHrDILAGgpAgpaxYjuSfr5oVVmH/nvWhWU8kBBAMDJI6Cg1Tw0+gz16WBXWU29st9brUY3U48BACeHgIJWExps1Z9v7K/I0CB9l3tQf/lim9klAQDaCQIKWlWnxEg9fWgp/D8v2Kbvcg+aXBEAoD0goKDVXd2/g64ZkCa3IWXPXKXS6jqzSwIA+DivB5SGhgb9+te/VmZmpsLDw9W5c2f97ne/k9vt9pxjGIaefPJJOZ1OhYeHa+TIkdqwYYO3S4EP+d2VWcpMjFRBWa0e+e9alsIHAJyQ1wPKM888o9dee03Tpk3Tpk2b9Oyzz+q5557TX/7yF885zz77rJ5//nlNmzZNy5cvV0pKii666CJVVLDyqL+KsgXrzzf2V0iQRXM37tXby3aZXRIAwId5PaB8++23uvLKKzVmzBh16tRJ1157rUaPHq0VK1ZIauo9efHFF/X444/rmmuuUVZWlt58801VV1frnXfe8XY58CG9O9g16ZIekqTfz96ozUXlJlcEAPBVXg8ow4cP14IFC7R161ZJ0po1a7R48WJddtllkqTc3FwVFRVp9OjRntfYbDaNGDFCS5YsOeZ7ulwulZeXN9vQPt0+PFPnn5Gkuga37n1nlWrqWAofAHA0rweUSZMmady4cerRo4dCQkLUv39/ZWdna9y4cZKkoqKmVUUdDkez1zkcDs+xI02dOlV2u92zpaene7tstBGLxaLnruurpGibthVX6nezN5pdEgDAB3k9oLz33nt6++239c4772jlypV688039X//93968803m51nsViafW8YxlH7Dps8ebLKyso8W35+vrfLRhtKjLLpxRv6yWKR3v1ulz5ZW2h2SQAAHxPs7Td8+OGH9eijj+rGG2+UJPXu3Vt5eXmaOnWqJkyYoJSUFElNPSmpqame1xUXFx/Vq3KYzWaTzWbzdqkw0TldE3XXiC569avv9egHa9U33a4OcRFmlwUA8BFe70Gprq6W1dr8bYOCgjzTjDMzM5WSkqJ58+Z5jtfV1WnhwoUaNmyYt8uBD3vgou7qnxGritoG3T9ztRoa3T/+IgBAQPB6QLn88sv1hz/8QZ988ol27typWbNm6fnnn9fVV18tqenWTnZ2tqZMmaJZs2Zp/fr1mjhxoiIiIjR+/HhvlwMfFhLUtBR+tC1YOXklemkBS+EDAJpYDC+vmFVRUaHf/OY3mjVrloqLi+V0OjVu3Dj99re/VWhoqKSm8SZPPfWU/vrXv6qkpERDhgzRyy+/rKysrJP6GeXl5bLb7SorK1NMTIw3y4cJPl5ToHvfXSWLRXrrtsE6t1uS2SUBAFpBSz6/vR5Q2gIBxf88+v5azVyer9iIEH10z3BlJDAeBQD8TUs+v3kWD3zCk1f0Ut/0WJVW1+vnM1aouq7B7JIAACYioMAnhIUE6bWbBygxyqbNRRV6+D9r5Xa3u849AICXEFDgM1Lt4Xrt5gEKCbLok3WFem7uFrNLAgCYhIACnzKoU7ymXtNHkvTqV9/r7aV5JlcEADADAQU+59qBHfSrUd0lSb/9f+u1YNNekysCALQ1Agp80n0XdtX1gzrIbUi/fGeV1uSXml0SAKANEVDgkywWi/5wdW+d1z1JNfWNuv3N5dp1oNrssgAAbYSAAp8VEmTVKzcNUM/UGO2vrNPE6d+ppKrO7LIAAG2AgAKfFmUL1j9vPUtOe5h27KvSHW+tUG19o9llAQBaGQEFPs8RE6bptw1WdFiwVuSV6MF/r2GNFADwcwQUtAvdHdH66y0DPWukTP1sk9klAQBaEQEF7cawLol67tq+kqQ3vs7V9G9yTa4IANBaCChoV67qn6aHLz5DkvTU7I2as6HI5IoAAK2BgIJ25+6RXTRucIYMQ7rv3VVauavE7JIAAF5GQEG7Y7FY9Psre+n8M5LkanDrZ2+u0M79VWaXBQDwIgIK2qXgIKumjR+grLQYHayq08R/fqcDlS6zywIAeAkBBe1WpC1Y/5h4ltJiw7XzQLV+xhopAOA3CCho15Kjw/TmbWfJHh6iVbtKdf/MVWpodJtdFgDgNBFQ0O51TY7W67cMVGiQVXM27NWv/r2GkAIA7RwBBX5hSOcETRvfX8FWiz5eU0BIAYB2joACvzG6V4peuWmAQoKaQkr2e6sJKQDQThFQ4FeaQkrTkviz1xbqfkIKALRLBBT4nYt6Ojwh5RNCCgC0SwQU+KWLejr06g9DyszVqiekAEC7QUCB3xr1w5CyrlD3z1xFSAGAdoKAAr82qqdDr93cNAX503VFhBQAaCcIKPB7F57p0Gu3DPCElPveJaQAgK8joCAgXNDjfyHls/WEFADwdQQUBIwLejj010Mrzn62vkj3vkNIAQBfRUBBQDm/R7InpHy+oUh3/2slDxgEAB9EQEHAOb9Hsv7604EKDbZq3sa9uvWfy1VRW292WQCAHyCgICCdf0ay3rx1sKJswfp2xwGNf2OZDlS6zC4LAHAIAQUBa2iXBL17x9mKjwzVuj1luu61b5V/sNrssgAAIqAgwPXuYNd/7hqqtNhw7dhfpatfWaL1e8rMLgsAAh4BBQGvS1KU3v/FMPVIidb+Spdu+Ou3Wrh1n9llAUBAI6AAklLsYfr3XUN1TtcEVdU16vbpy/XfnN1mlwUAAYuAAhwSExaif04crKv6OdXgNvTQf9boLwu2yTAMs0sDgIBDQAF+IDTYquev76e7RnSRJP1p3lY9/N+1qmtgQTcAaEsEFOAIVqtFj17aQ09flSWrRfpvzm7d/PdlOlhVZ3ZpABAwCCjAcdx8dkf9Y+JZirYF67vcg7rq5W+0vbjC7LIAICAQUIATGHlGsj64e5jS48O162C1rn55ib7aUmx2WQDg9wgowI/o5ojWh3efo7M6xanC1aDbpi/X64u+Z/AsALQiAgpwEhKibHr7Z0N0w6B0uQ1pyqeb9cC/1/CgQQBoJQQU4CTZgoP0x5/01lNX9FKQ1aJZq/boute+1e4SlscHAG8joAAtYLFYNGFYJ824fbDiIkK0bk+ZLv/LYi3ett/s0gDArxBQgFMwrEuiPr53uHqn2VVSXa+f/mOZXvlqO+NSAMBLCCjAKeoQF6H/3DVU1w3sILchPfv5Fv18Ro7KaurNLg0A2j0CCnAawkKC9Oy1fTTl6t4KDbJq3sa9GvPnr7VyV4nZpQFAu0ZAAU6TxWLR+CEZev8XTeul7C6p0XWvfauXv9yuRje3fADgVBBQAC/p3cGuT+47V1f0darRbei5OVt009+Wqqis1uzSAKDdIaAAXhQTFqKXbuyn/7uuryJCg7R0x0Fd8tIizd1QZHZpANCuEFAAL7NYLLp2YAfNPjTLp7S6Xj+fkaPffLiehd0A4CQRUIBW0jkpSu//Yph+fl5nSdKMpXm6cto32lLEAwcB4McQUIBWFBps1WOXnak3bxusxCibtuyt0BXTFmvG0jzWTAGAEyCgAG1gRPckfZ59rkaekSRXg1u/+XC97pyRo4NVdWaXBgA+iYACtJHEKJv+MeEs/WZsT4UGWTV3416NfmGh5jCAFgCOQkAB2pDVatHtwzP1wd3D1N0Rpf2VdbpzRo5+9d5qlVWzAi0AHNYqAWXPnj26+eablZCQoIiICPXr1085OTme44Zh6Mknn5TT6VR4eLhGjhypDRs2tEYpgE/KSrPr43uH6xcju8hqkWat2qOLXlioBZv2ml0aAPgErweUkpISnXPOOQoJCdFnn32mjRs36k9/+pNiY2M95zz77LN6/vnnNW3aNC1fvlwpKSm66KKLVFHB7AYEDltwkCZd0kP//cUwdU6KVHGFS7e/uUL3vbtKBypdZpcHAKayGF6eSvDoo4/qm2++0ddff33M44ZhyOl0Kjs7W5MmTZIkuVwuORwOPfPMM7rzzjt/9GeUl5fLbrerrKxMMTEx3iwfMEVtfaOen7dVf/t6h9yGFBcRoicu76Ur+zllsVjMLg8AvKIln99e70H56KOPNGjQIF133XVKTk5W//799cYbb3iO5+bmqqioSKNHj/bss9lsGjFihJYsWXLM93S5XCovL2+2Af4kLCRIj112pj685xz1SIlWSXW9st9brdumL9ee0hqzywOANuf1gLJjxw69+uqr6tatm+bMmaO77rpL9913n9566y1JUlFR04wFh8PR7HUOh8Nz7EhTp06V3W73bOnp6d4uG/AJfTrE6uN7h+uh0d0VGmTVl1v26aLnF+r1Rd+rvtFtdnkA0Ga8HlDcbrcGDBigKVOmqH///rrzzjt1xx136NVXX2123pHd1oZhHLcre/LkySorK/Ns+fn53i4b8BkhQVb98oJu+vT+czU4M17VdY2a8ulmXf6XxVqx86DZ5QFAm/B6QElNTVXPnj2b7TvzzDO1a9cuSVJKSookHdVbUlxcfFSvymE2m00xMTHNNsDfdU2O0ns/P1vPXdtH8ZGh2lxUoWtf+1aP/HcNC7wB8HteDyjnnHOOtmzZ0mzf1q1b1bFjR0lSZmamUlJSNG/ePM/xuro6LVy4UMOGDfN2OUC7ZrFYdN2gdC14YIRuPKvp1ua/V+zWBX/6SjOW5qnRzXL5APyT1wPKr371Ky1dulRTpkzR9u3b9c477+j111/XPffcI6npH9zs7GxNmTJFs2bN0vr16zVx4kRFRERo/Pjx3i4H8AtxkaH640/66P1fDFWPlGiVVtfrNx+u19i/LNayHQfMLg8AvM7r04wlafbs2Zo8ebK2bdumzMxMPfDAA7rjjjs8xw3D0FNPPaW//vWvKikp0ZAhQ/Tyyy8rKyvrpN6facYIZA2Nbv1r2S49P2+rymqaVp8d0ydVj112ptJiw02uDgCOryWf360SUFobAQWQDlbV6fl5W/TOsl1yG1JYiFV3jeiiO8/rovDQILPLA4CjEFCAALKxoFxPfrxB3+U2zfBJiQnTry7qpp8M6KDgIB63BcB3EFCAAGMYhj5ZV6ipn272LOzWLTlKj1zSQ6POTGY1WgA+gYACBChXQ6NmfJunaV9uV+mhpyOf1SlOj17aQwM7xptcHYBAR0ABAlx5bb1e++p7/eObXNXWN61AO7qnQ49c0kNdk6NMrg5AoCKgAJAkFZXV6sX5W/XvFflyG5LVIt1wVrqyR3WXIybM7PIABBgCCoBmtu2t0LNztmjexr2Smmb83HpOpu44t7PiI0NNrg5AoCCgADim5TsP6o+fbVZOXokkKSI0SBOGdSKoAGgTBBQAx2UYhuZvKtaL87dqQ0G5pKag8tOhnXTHuZlKiLKZXCEAf0VAAfCjDgeVlxZs1fo9/wsqt5zdUXec11mJBBUAXkZAAXDSDMPQgk3FemnBNq3bUyZJCg8J0i1DO+qOczsrKZqgAsA7CCgAWswwDH25pVgvzt+mtbubgoot2KobzkrXHed2Vnp8hMkVAmjvCCgATplhGPpqyz69tGCbVueXSpKCrBaN7ZOqO8/rop5O/s4BODUEFACnzTAMffv9Ab268Ht9vW2/Z/+I7km687zOGtolgSX0AbQIAQWAV63fU6bXFn6vT9cVyn3oX4xezhj97NxMjentVGgwDyUE8OMIKABaRd6BKv3t61z9Jyffs4S+I8amnw7tpPGDMxTHWioAToCAAqBVlVTV6Z3vdmn6kp3aV+GS1LQ67dX90zRhWCf1SOHvJYCjEVAAtAlXQ6NmrynUP77J9Sz6JjU9QfnmszvqkqwU2YKDTKwQgC8hoABoU4ZhaPnOEv3zm1zN3bhXjYcGqsRHhuq6QR100+COykhgmjIQ6AgoAExTVFar95bn693vdqmovNaz/7zuSbp5SIYu6JGs4CAG1QKBiIACwHQNjW4t2Fysfy3bpUVb93n2p9rDdONZGbpxcLocMWEmVgigrRFQAPiUvANVemfZLv17Rb5KquslNS3+dtGZDo0bkqHhXRMVZGVNFcDfEVAA+KTa+kZ9vr5Iby/N04q8Es9+R4xNV/VL09UD0pgBBPgxAgoAn7e5qFzvLtulD1cXqKym3rO/Z2qMrhmQpiv6OZUczS0gwJ8QUAC0G3UNbn25pVgfrNytLzYXq76x6Z8kq0U6t1uSrhmQptE9UxQeynRloL0joABol0qq6jR7XaFmrdytlbtKPfujbMG6JCtF1wxI09mZCbIyXgVolwgoANq93P1VmrVqj2at2q38gzWe/U57mK7qn6ZrBqSpa3K0iRUCaCkCCgC/YRiGVuSV6IOVuzV7baEqahs8x/p0sOvKfmka0ztVKXbGqwC+joACwC/V1jdqwaZizVq1W19t2aeGQyvWWizSWR3jNaZPqi7NSlEy66sAPomAAsDvHah06eM1BZq9trDZlOXDYeXS3im6JCtFqfZwE6sE8EMEFAABpaC0Rp+tL9InawuaDa6VpH7psbokK0UX90pRZmKkOQUCkERAARDA9pTW6PP1Rfp8fVPPyg//hTvDEa2Lezl0Uc8UZaXFyGJhNhDQlggoACCpuLxWczYUac6GvVq644BnzIrU9EygUWc6dFFPh4Z0jpctmHVWgNZGQAGAI5RV12vB5r2au2GvFm3bp+q6Rs+xyNAgndstSRf0SNbIM5IYZAu0EgIKAJxAbX2jlny/X/M27tX8TcXaV+FqdjwrLUYXnJGskT2S1bdDLA8yBLyEgAIAJ8ntNrRuT5m+2Fysr7YUa83usmbH4yNDNaJ7ks7vkazhXRMVHxlqUqVA+0dAAYBTtK/CpYVb9+nLzcVatHWfKlz/WxjOYpF6p9l1brdEndctSf0z4hQabDWxWqB9IaAAgBfUN7qVk1eiL7cUa+GWfdpcVNHseGRokIZ2SdB53ZM0vGuiMhMjmRkEnAABBQBaQXF5rb7etl+Ltu3T4m37daCqrtnxVHuYzumaqHO6JujszgksEgccgYACAK3M7Ta0sbBci7bt09db9ysnr0R1je5m53RKiNDZnRM8G88LQqAjoABAG6upa9SKvINavH2/ln5/QOv2lMl9xL+uBBYEOgIKAJisorZeK3aWaOmOA1q649iBJTMxUmd3jteQzAQNzoyXM5ZbQvBvBBQA8DHltfVasfOglu44qKU7Dmj9MQJLWmy4zuoUp0Gd4nVWp3h1S46SlTVY4EcIKADg444MLBsKytV4RGKJCQvWgI5xGtQxTgMy4tQ3PVaRtmCTKgZOHwEFANqZSleDVu8q1Xc7D2rFzoNanV/abDl+SbJapB4pMRrQMVb90+PUPyOWqc1oVwgoANDONTS6tamwQivyDionr0SrdpVqT2nNUefZw0PULz22acuIVb8OsYpjtVv4KAIKAPihorJardxVopV5JVqdX6p1e8rkanAfdV5GfIT6pseqbwe7+qbHqpczRhGh3BqC+QgoABAA6hvd2lxYoVX5TT0sa/JLtWN/1VHnWS1St+RoZaXZ1aeDXVlpdvVMjVF4aJAJVSOQEVAAIECVVddr7Z5Srd1dpjX5pVqzu1R7y11HnRdktahrUpR6pcWol9OuXs4Y9XTGKCYsxISqESgIKAAAj73ltVq3u0zr9jRta3eXaX/l0aFFaro91MsZc2izq6czRsnRNgbiwisIKACA4zIMQ3vLXVq/p0zrC8q0oaBcGwvKjzkIV5LiIkLUIyVGPVKj1SMlWj1SYtTdEc0tIrQYAQUA0GIlVXXaWFiuDT8ILd/vqzxqQTlJslikTgmR6pESrTMOhZYzU6OVHhfB4nI4LgIKAMArausbtW1vpTYXlWtzUUXT18KKo57kfFhEaJC6O6LV3RGlbsnR6uaIUndHtFLtYdwmAgEFANC69lW4tLmoXFuKKrSpsCm4bCuuVN0xpj1LUrQtWF0dUep+KLR0SY5St+QoOe3h9LgEEAIKAKDNNTS6tfNAlTYXVWjb3kptK67Q1r2V2rm/Sg3Huk8kKTwkSF2SI9U1KUpdkpqCS5ekKHVMiFBYCGNc/E1LPr9ZuQcA4BXBQVZ1TY5W1+ToZvvrGpqCy9a9TYFle3GFthdXKnd/lWrqG7V+T7nW7ylv9hqLRUqPi1DnpEh1SYpSp8RIdUqIUKeESDljwxVEr4vfowcFAGCK+ka3dh2s1vbiSm0vrtT3+yq1Y1+Vvt9XqYrahuO+LiTIovT4CGUmRKpjQqQ6JTYFl6bwEqbgIGsbtgItwS0eAEC7ZRiG9lfWeQLLjn2V2nmgSjsPVGvXgWrVNR57nIskBVubwkunhIim8JIQcaj3JVJpceEKIbyYils8AIB2y2KxKCnapqRom87unNDsWKPbUGFZjfIOVDeFlv1NwSXvUICpa3Ard3+VcvdXSdrX7LXBVos6xIV7gsvh3peM+Ah1iGPMi69p9R6UqVOn6rHHHtP999+vF198UVJTOn7qqaf0+uuvq6SkREOGDNHLL7+sXr16ndR70oMCADiS222oqLz2UHBpCi25+6s8YeZYD1b8oeRom9LjmwJLely4OsRFqEN8uNLjIpRq59aRN/hMD8ry5cv1+uuvq0+fPs32P/vss3r++ec1ffp0de/eXU8//bQuuugibdmyRdHR0cd5NwAAjs9qtcgZGy5nbLiGdWl+zO02tLei9n/B5UCV8vY3BZfdJTWqdDWouMKl4gqXcvJKjnrvIKtFKTFhSosLV4e4cHWIbQowaXHhSosNV2psmGzB9MB4U6v1oFRWVmrAgAF65ZVX9PTTT6tfv3568cUXZRiGnE6nsrOzNWnSJEmSy+WSw+HQM888ozvvvPNH35seFACAtxiGodLqeu06WK38kmrlH6w59LVae0pqtLuk5oTjXg5LirbJGRuutNgwOe3hnrCUFhsuZ2yY4iNDA36xOp/oQbnnnns0ZswYjRo1Sk8//bRnf25uroqKijR69GjPPpvNphEjRmjJkiXHDCgul0su1/8ebFVeXn7UOQAAnAqLxaK4yFDFRYaqb3rsUcfdbkP7Kl3aXVKj3SXV2lNa4wkue0qb9tXWu7WvwqV9FS6tyT/2z7EFW5VqD1OqPbzpa2yYUuzhctrDlHJof1xESMCHmMNaJaDMnDlTK1eu1PLly486VlRUJElyOBzN9jscDuXl5R3z/aZOnaqnnnrK+4UCAPAjrFaLHDFhcsSEaWDHuKOOH+6B2VNao4LSGs/XgtJaz5+LK1xyNbi180C1dh6oPu7PCj0UYhwxYUqJaQou//uzTY6YMCVHhyk02P/Hw3g9oOTn5+v+++/X3LlzFRYWdtzzjkyIhmEcNzVOnjxZDzzwgOf78vJypaene6dgAABOww97YLLS7Mc8x9XQqL1lLhWW1aiwrPbQVuP5WlRWq/2VdaprcCvvQLXyThBiJCkhMlTJMWFKjrbJEXM4uNiUfChIJR+aBdWep1V7PaDk5OSouLhYAwcO9OxrbGzUokWLNG3aNG3ZskVSU09Kamqq55zi4uKjelUOs9lsstls3i4VAIA2YQsOUkZChDISIo57Tm19o/ZVuFRYVqui8lrtPfT1h38uLneprtGtA1V1OlBVp02Fx/+ZFosUHxGqpEPBJSnK5pm+nRRt84SYpGibom3BPndryesB5cILL9S6deua7bv11lvVo0cPTZo0SZ07d1ZKSormzZun/v37S5Lq6uq0cOFCPfPMM94uBwCAdiEsJEjp8RFKjz9+iDEMQwer6jwzjvaW16q4vFZ7y10qrjj0tbxWxRUuNbgNT5DZXFRxwp9tC7YqKdqmxEMhJjHKpoz4CP1iZJcTvq41eT2gREdHKysrq9m+yMhIJSQkePZnZ2drypQp6tatm7p166YpU6YoIiJC48eP93Y5AAD4DYvFooQomxKibDoz9fjnud2GSqrrVFRe6xm8u6/S9b8//+D7itoGuRrchwYB13jeo3NipH8FlJPxyCOPqKamRnfffbdnoba5c+eyBgoAAF5gtf4vyPyYmrpG7a9s6oHZV1Gn/ZUu7a90Kcpm7mLzPIsHAAC0iZZ8frff4b0AAMBvEVAAAIDPIaAAAACfQ0ABAAA+h4ACAAB8DgEFAAD4HAIKAADwOQQUAADgcwgoAADA5xBQAACAzyGgAAAAn0NAAQAAPoeAAgAAfI65z1I+RYcfwFxeXm5yJQAA4GQd/tw+/Dl+Iu0yoFRUVEiS0tPTTa4EAAC0VEVFhex2+wnPsRgnE2N8jNvtVkFBgaKjo2WxWLz63uXl5UpPT1d+fr5iYmK8+t7tQaC3X+IaBHr7Ja6BxDUI9PZLrXMNDMNQRUWFnE6nrNYTjzJplz0oVqtVHTp0aNWfERMTE7C/lBLtl7gGgd5+iWsgcQ0Cvf2S96/Bj/WcHMYgWQAA4HMIKAAAwOcQUI5gs9n0xBNPyGazmV2KKQK9/RLXINDbL3ENJK5BoLdfMv8atMtBsgAAwL/RgwIAAHwOAQUAAPgcAgoAAPA5BBQAAOBzCCgAAMDnBGRAefXVV9WnTx/P6nhDhw7VZ5995jluGIaefPJJOZ1OhYeHa+TIkdqwYYOJFbeuqVOnymKxKDs727PP36/Bk08+KYvF0mxLSUnxHPf39h+2Z88e3XzzzUpISFBERIT69eunnJwcz3F/vg6dOnU66nfAYrHonnvukeTfbT+soaFBv/71r5WZmanw8HB17txZv/vd7+R2uz3n+Pt1qKioUHZ2tjp27Kjw8HANGzZMy5cv9xz3t/YvWrRIl19+uZxOpywWiz788MNmx0+mvS6XS/fee68SExMVGRmpK664Qrt37/Z+sUYA+uijj4xPPvnE2LJli7FlyxbjscceM0JCQoz169cbhmEYf/zjH43o6Gjj/fffN9atW2fccMMNRmpqqlFeXm5y5d733XffGZ06dTL69Olj3H///Z79/n4NnnjiCaNXr15GYWGhZysuLvYc9/f2G4ZhHDx40OjYsaMxceJEY9myZUZubq4xf/58Y/v27Z5z/Pk6FBcXN/vvP2/ePEOS8eWXXxqG4d9tP+zpp582EhISjNmzZxu5ubnGf/7zHyMqKsp48cUXPef4+3W4/vrrjZ49exoLFy40tm3bZjzxxBNGTEyMsXv3bsMw/K/9n376qfH4448b77//viHJmDVrVrPjJ9Peu+66y0hLSzPmzZtnrFy50jj//PONvn37Gg0NDV6tNSADyrHExcUZf/vb3wy3222kpKQYf/zjHz3HamtrDbvdbrz22msmVuh9FRUVRrdu3Yx58+YZI0aM8ASUQLgGTzzxhNG3b99jHguE9huGYUyaNMkYPnz4cY8HynU47P777ze6dOliuN3ugGn7mDFjjNtuu63Zvmuuuca4+eabDcPw/9+B6upqIygoyJg9e3az/X379jUef/xxv2//kQHlZNpbWlpqhISEGDNnzvScs2fPHsNqtRqff/65V+sLyFs8P9TY2KiZM2eqqqpKQ4cOVW5uroqKijR69GjPOTabTSNGjNCSJUtMrNT77rnnHo0ZM0ajRo1qtj9QrsG2bdvkdDqVmZmpG2+8UTt27JAUOO3/6KOPNGjQIF133XVKTk5W//799cYbb3iOB8p1kKS6ujq9/fbbuu2222SxWAKm7cOHD9eCBQu0detWSdKaNWu0ePFiXXbZZZL8/3egoaFBjY2NCgsLa7Y/PDxcixcv9vv2H+lk2puTk6P6+vpm5zidTmVlZXn9mgRsQFm3bp2ioqJks9l01113adasWerZs6eKiookSQ6Ho9n5DofDc8wfzJw5UytXrtTUqVOPOhYI12DIkCF66623NGfOHL3xxhsqKirSsGHDdODAgYBovyTt2LFDr776qrp166Y5c+borrvu0n333ae33npLUmD8Hhz24YcfqrS0VBMnTpQUOG2fNGmSxo0bpx49eigkJET9+/dXdna2xo0bJ8n/r0N0dLSGDh2q3//+9yooKFBjY6PefvttLVu2TIWFhX7f/iOdTHuLiooUGhqquLi4457jLcFefbd25IwzztDq1atVWlqq999/XxMmTNDChQs9xy0WS7PzDcM4al97lZ+fr/vvv19z58496v8cfsifr8Gll17q+XPv3r01dOhQdenSRW+++abOPvtsSf7dfklyu90aNGiQpkyZIknq37+/NmzYoFdffVU//elPPef5+3WQpL///e+69NJL5XQ6m+3397a/9957evvtt/XOO++oV69eWr16tbKzs+V0OjVhwgTPef58HWbMmKHbbrtNaWlpCgoK0oABAzR+/HitXLnSc44/t/9YTqW9rXFNArYHJTQ0VF27dtWgQYM0depU9e3bVy+99JJnJseRSbC4uPioVNle5eTkqLi4WAMHDlRwcLCCg4O1cOFC/fnPf1ZwcLCnnf58DY4UGRmp3r17a9u2bQHxOyBJqamp6tmzZ7N9Z555pnbt2iVJAXMd8vLyNH/+fP3sZz/z7AuUtj/88MN69NFHdeONN6p379665ZZb9Ktf/crTsxoI16FLly5auHChKisrlZ+fr++++0719fXKzMwMiPb/0Mm0NyUlRXV1dSopKTnuOd4SsAHlSIZhyOVyeX4p582b5zlWV1enhQsXatiwYSZW6D0XXnih1q1bp9WrV3u2QYMG6aabbtLq1avVuXNnv78GR3K5XNq0aZNSU1MD4ndAks455xxt2bKl2b6tW7eqY8eOkhQw1+Gf//ynkpOTNWbMGM++QGl7dXW1rNbmHwNBQUGeacaBch2kpv9JSU1NVUlJiebMmaMrr7wyoNovndx/74EDByokJKTZOYWFhVq/fr33r4lXh9y2E5MnTzYWLVpk5ObmGmvXrjUee+wxw2q1GnPnzjUMo2mald1uNz744ANj3bp1xrhx49r1tLKT8cNZPIbh/9fgwQcfNL766itjx44dxtKlS42xY8ca0dHRxs6dOw3D8P/2G0bTFPPg4GDjD3/4g7Ft2zbjX//6lxEREWG8/fbbnnP8/To0NjYaGRkZxqRJk4465u9tNwzDmDBhgpGWluaZZvzBBx8YiYmJxiOPPOI5x9+vw+eff2589tlnxo4dO4y5c+caffv2NQYPHmzU1dUZhuF/7a+oqDBWrVplrFq1ypBkPP/888aqVauMvLw8wzBOrr133XWX0aFDB2P+/PnGypUrjQsuuIBpxt5y2223GR07djRCQ0ONpKQk48ILL/SEE8Nommr1xBNPGCkpKYbNZjPOO+88Y926dSZW3PqODCj+fg0Oz+0PCQkxnE6ncc011xgbNmzwHPf39h/28ccfG1lZWYbNZjN69OhhvP76682O+/t1mDNnjiHJ2LJly1HH/L3thmEY5eXlxv33329kZGQYYWFhRufOnY3HH3/ccLlcnnP8/Tq89957RufOnY3Q0FAjJSXFuOeee4zS0lLPcX9r/5dffmlIOmqbMGGCYRgn196amhrjl7/8pREfH2+Eh4cbY8eONXbt2uX1Wi2GYRje7ZMBAAA4PYxBAQAAPoeAAgAAfA4BBQAA+BwCCgAA8DkEFAAA4HMIKAAAwOcQUAAAgM8hoAAAAJ9DQAEAAD6HgAIAAHwOAQUAAPic/w9XEl80SUEwCQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X1_sort = X1.sort_values()\n",
    "\n",
    "a = theta4\n",
    "b = theta5 * X1_sort + theta2\n",
    "c = theta0 + theta1 * X1_sort + theta3 * X1_sort * X1_sort\n",
    "X2_new_boundary = (-b+np.sqrt(b*b-4*a*c))/(2*a)\n",
    "\n",
    "fig7 = plt.figure()\n",
    "print(X1, X1_sort)\n",
    "plt.plot(X1_sort,X2_new_boundary)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "8bc23a85-89d2-4c93-8a2b-19f406de69db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig8 = plt.figure()\n",
    "\n",
    "\n",
    "X1_sort = X1.sort_values()\n",
    "a = theta4\n",
    "b = theta5 * X1_sort + theta2\n",
    "c = theta0 + theta1 * X1_sort + theta3 * X1_sort * X1_sort\n",
    "X2_new_boundary = (-b+np.sqrt(b*b-4*a*c))/(2*a)\n",
    "\n",
    "passed = plt.scatter(data.loc[:,'Exam1'][mask], data.loc[:,'Exam2'][mask],c='green',s=5)\n",
    "failed = plt.scatter(data.loc[:,'Exam1'][~mask], data.loc[:,'Exam2'][~mask],c='pink',s=5)\n",
    "plt.title('Exam1 - Exam2')\n",
    "plt.xlabel('Exam1')\n",
    "plt.ylabel('Exam2')\n",
    "plt.legend((passed,failed),('passed','failed'))\n",
    "plt.plot(X1_sort,X2_new_boundary,c='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f55c2010-1cd6-4f1a-a320-7bb619ad84b9",
   "metadata": {},
   "source": [
    "* 边界函数\n",
    "$$\n",
    "w_1 x_1 + w_2 x_2 + b = 0\n",
    "$$\n",
    "\n",
    "* 二级边界函数\n",
    "$$\n",
    "\\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\theta_3 x_1^2 + \\theta_4 x_2^2 + \\theta_5 x_1 x_2 = 0\n",
    "$$\n",
    "\n",
    "* 二阶边界函数的标准形式\n",
    "$$\n",
    "\\theta_3 x_1^2 + (\\theta_1 + \\theta_5 x_2) x_1 + (\\theta_0 + \\theta_2 x_2 + \\theta_4 x_2^2) = 0\n",
    "$$\n",
    "\n",
    "* 求解x\n",
    "$$\n",
    "x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0ad4aa4c-5547-4dfb-bc93-43080d9a0ef0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1856a05a-442f-4731-a815-c0930f52b372",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "42b9ceb3-f172-43df-9e86-8b7ec6c98394",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "26a0c285-a5c4-4426-80b8-0ee3e5d9d391",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "e79c9a32-5034-4c48-af14-0ef5abb97cdf",
   "metadata": {},
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "04f60036-2a6e-4be1-9172-d33293ae1d45",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "18df5483-13b8-4d3a-8928-bfbdf7aa3b2a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "232054dd-820c-4381-b327-9aa77e693f78",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ce6baf49-c4ab-4f1f-850e-53486d548008",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7cb2c877-9f19-45a5-bdaa-881b0c3e21cb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8a948354-2821-44d6-84df-2509db58a2fd",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dad21093-e715-4b54-af25-9bcaaa93e430",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4fe60bff-afdc-4db8-aab2-e0fcca38324a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "847f6d6a-1042-4b65-8fff-12b1a20c7e30",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "81ff76f8-7550-4690-89dd-99a03a945648",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "048f6771-a2b7-46f7-9767-4a448d79b46e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "80d48017-1f11-422f-93be-8a93f01a6a42",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6b562415-a9ba-4b42-97e5-9671b3ce4cef",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "de88657e-3a43-4ac3-8d97-1cb18470a079",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "035d3508-06a2-45b1-bb11-d72bf17338cb",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
